Fig. 1. System block diagram. The system is composed of two phases, namely training and testing. (a) presents the block diagram for the testing phase. A test image is given to the system that determines if it is a replica of a given reference image contained in the database. The method can be decomposed into two distinct parts: the upper part of (a) shows steps that are independent from the reference image while the lower part of (a) depicts steps that depend on the reference image. (b) depicts the block diagram for the training phase of a single reference image. The features f_ref of the reference image, the training examples {f_i}_i, and the corresponding labels {y_i}_i are fed to the training algorithm that produces the parameters of the steps depending on the reference image.

Fig. 2. Examples of test replicas. (a) is the original while (b) represents examples of test replicas. There is one replica example per category, the order used is the same than in the text (left–right, top–down).

Fig. 3. Influence of ρ. All curves used a fixed number of dimensions d=50, only the value of ρ is changed. (a) shows the  curve for ρ=1, as well as the equal error rate (EER) curve. (b) depicts the vertical differences between the  curves corresponding to ρ={10²,10⁴,10⁶} and that corresponding to ρ=1.

Fig. 4. False negative histograms. For a fixed false positive rate r_fp=5×10^-5 (leftmost value of the curves in Fig. 3), number of dimensions d=50, and two different values of ρ.

Fig. 5. Influence of grey-level features.  curves with, and without, using grey-level features. The equal error rate (EER) curve is also shown.

Fig. 6. Influence of the weighted inter-image differences.  curves for s_α=0 and optimised s_α. The equal error rate (EER) curve is also shown.

Fig. 7. Influence of the dimensionality reduction.  curves for different values of d. The equal error rate (EER) curve is also shown.

Fig. 8. Comparison with other methods. The proposed method is compared against other methods: KPs [18] and DPF [30]. The equal error rate (EER) curve is also shown.

Training replicas generation

Image operations and their parameters.

Features overview

List the types of used features and the number of extracted statistics.

 curve precision

The precision is obtained by taking into account the number of test examples (18,085 for the non-replicas, and 40 for the replicas), and the number of individual DET curves used for averaging (200).

Storage requirements estimation

Real number are coded on 16 bits (two bytes). The number of dimensions after dimensionality reduction is 50. In our experiment (using d=50 and ρ=10⁴), the average number of support vectors is found to be about 85.

Average running time for testing

The experiments were carried out on a PC with a 2.8 GHz processor and 1 Go of RAM.